Realistic Controls

  • Alexander B. KurzhanskiEmail author
  • Alexander N. Daryin
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 468)


The present chapter describes the realistic controls that approximate the earlier found ideal impulsive functions. This is reduced to the description of the dynamic programming under double constraints.


  1. 1.
    Crandall, M.G., Lions, P.L.: Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277(1), 1–41 (1983)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Daryin, A.N., Kurzhanski, A.B.: Impulse control inputs and the theory of fast controls. In: Proceedings of 17th IFAC World Congress, pp. 4869–4874. IFAC, Seoul (2008)Google Scholar
  3. 3.
    Fan, Ky: Mini max theorems. Proc. Natl. Acad. Sci. USA 39(1), 42–47 (1953)Google Scholar
  4. 4.
    Filippov, A.F.: Differential Equations with Discontinuous Righthand Sides. Kluwer, Dordrecht (1988)CrossRefGoogle Scholar
  5. 5.
    Fleming, W.H., Soner, H.M.: Controlled Markov Processes and Viscosity Solutions. Springer, New York (1993)zbMATHGoogle Scholar
  6. 6.
    Gel’fand, I.M., Shilov, G.E.: Generalized Functions. Volume I: Properties and Operations. Academic Press, New York (1964)zbMATHGoogle Scholar
  7. 7.
    Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Pergamon Press, Oxford (1982)zbMATHGoogle Scholar
  8. 8.
    Kolmogorov, A.N., Fomin, S.V.: Introductory Real Analysis. Dover Publications, New York (1975)Google Scholar
  9. 9.
    Schwartz, L.: Théorie des Distributions. Hermann, Paris (1950)zbMATHGoogle Scholar
  10. 10.
    Schwartz, L.: Méthodes Mathématiques Pour les Sciences Physiques. Hermann, Paris (1961)zbMATHGoogle Scholar
  11. 11.
    Stengel, R.F.: Optimal Control and Estimation. Dover Pub. Inc., New York (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  • Alexander B. Kurzhanski
    • 1
    Email author
  • Alexander N. Daryin
    • 2
  1. 1.Faculty of Computational Mathematics and CyberneticsLomonosov Moscow State UniversityMoscowRussia
  2. 2.Google ResearchZürichSwitzerland

Personalised recommendations